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In this talk, I will discuss our work on remeshing manifolds of arbitrary genus.In particular, I will focus on the problem of remeshing 2-manifold surfaces with quadrilaterals. This is a problem of fundamental importance in surface parameterization, subdivision surface modelling, and computational fluid dynamics, among other applications. Our remeshing scheme is both efficient and flexible, and produces an output mesh composed entirely of well-shaped quadrilaterals with very few extraordinary points. At the heart of this method is our Morse-theoretic analysis of the eigenfunctions of the Laplace-Beltrami operator on piecewise-linear manifolds. This induces a decomposition of the surface into quadrangular patches that arises quite naturally from its intrinsic geometry. The meshes we produce faithfully preserve the structure of the original shape, and are quite well-suited for use in constructing Catmull-Clark subdivision surfaces.

More details can be found in our SIGGRAPH 2006 paper.